Lesson # 58: Permutations Involving Identical Objects

Objective: to find the number of permutation of n object when some of the objects are identical.

1) The permutations of the 4 different letter A, B, E and F are:

4! = 24

2) What happens if two of the letter are the same? Investigate this by converting each F to and E in the list below. Then count the number of permutations of the letters A, B, B and E.

4! = 12

2!

3) What happens if three of the letter are the same? Investigate this by converting each F and E to a B in the list below. Then count the number of permutations of the letters A, B, B and E.

4! = 4

3!

4a) A, B, C, D, D = 5! = 60
                                2!
b) A, B, B, D, D =   5!  = 30
                             2!x2!
Generalization:  The number of permutations of n objects of which there are a objects alike of one kind, b alike of another kind, c alike of another kind, and so one, is...      n!   
                                                                                              a! b! c!

        8!          

2!x2!x2!x2!